Squawk, no need to take full fuel just to avoid paying Tassy prices. Take what you need and then some, no problem. But I would say, on face value, without any extenuating circumstances, that 3100lbs is excessive for that kind of trip- especially in the commercial world (unless you disregard W&B, which some do). 3100 isn't full fuel anyway.
I'd quite comfortably do that trip, with no weather requirements, with 2100lbs. That's a bit over 30 mins margin on top of 30 fixed back at Essendon. Not exactly scary. Or to make life easy, full mains 2400lbs- gives me another 40mins margin back at EN plus no worries with the payload. Plenty of alternate and divert options.
And if you are likely to need fuel in Tas, build it into the charter cost!
Note- I'm basing the above two paragraphs on the assumption that it was just an EN-KI-EN trip.
Hell, you can take a B200 most of the way across the country with 3100lbs!
In relation to the rudder trim setting- the only real reasons why it would be there are- single engine flight (you still don't need full deflection); maintenance; or checking the full travel on pre-flight and forgetting to set it back to neutral afterwards.
outnabout- probably the only thing I don't like about the B200 is its payload when you stuck heaps of fuel in there. That's where the 350 is better. You'll find a lot of B200s are around the 3700-3800kg range empty. Varies a lot though with interiors, props (3 or 4 blade), other airframe and performance mods, landing gear, avionics fitouts (going from a standard avionics panel to a full glass can save about 60kg) etc etc.
VIP/executive type interiors (which ZCR had) are typically heavier than the "commuter" type configurations. The only one I flew with VIP config was about 100kg heavier, and that was just in the seats!